4. The following contingency table represents motor vehicle use in North America by country and vehicle type in 2016. Country Vehicle Type United States C1 Canada C2 Mexico C3 Total Automobiles V1 112,961 22,410 11,239 146,610 Buses V2 976 91 303 1,370 Motorcycles V3 8,680 716 2,053 11,449 Trucks V4 146,182 1,053 6,201 153,436 Total 268,799 24,270 19,796 312,865 g. Create a Joint Probability Table: ALL PROBABILITIES to 4 decimal places. Country Vehicle Type United States C1 Canada C2 Mexico C3 Total Automobiles V1 Buses V2 Motorcycles V3 Trucks V4 Total h. In words, what is event C1? i. In words, what is event V4? j. In words, what is event C1 ∩∩ V4 ? k. Find P(C1) l. Find P(V4) m. Find P(C1 ∩∩ V4) n. Find P(C1 ∪∪ V4) o. Find P(C1|V4) p. Find P(V4|C1)
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
4. The following contingency table represents motor vehicle use in North America by country and vehicle type in 2016.
| Country | Vehicle | Type | ||
|---|---|---|---|---|
| United States C1 | Canada C2 | Mexico C3 | Total | |
| Automobiles V1 | 112,961 | 22,410 | 11,239 | 146,610 |
| Buses V2 | 976 | 91 | 303 | 1,370 |
| Motorcycles V3 | 8,680 | 716 | 2,053 | 11,449 |
| Trucks V4 | 146,182 | 1,053 | 6,201 | 153,436 |
| Total | 268,799 | 24,270 | 19,796 | 312,865 |
g. Create a Joint Probability Table: ALL PROBABILITIES to 4 decimal places.
| Country | Vehicle | Type | ||
|---|---|---|---|---|
| United States C1 | Canada C2 | Mexico C3 | Total | |
| Automobiles V1 | ||||
| Buses V2 | ||||
| Motorcycles V3 | ||||
| Trucks V4 | ||||
| Total |
h. In words, what is
i. In words, what is event V4?
j. In words, what is event C1 ∩∩ V4 ?
k. Find P(C1)
l. Find P(V4)
m. Find P(C1 ∩∩ V4)
n. Find P(C1 ∪∪ V4)
o. Find P(C1|V4)
p. Find P(V4|C1)
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